Crossword Genius

Docs here in charge after Kay leaves prison (6)

Ross

I believe the answer is:

clinic

I'm a little stuck... Click here to teach me more about this clue!

'docs here in charge' is the definition.
Although both the answer and definition are singular nouns, I can't understand how one could define the other.

'after kay leaves prison' is the wordplay.
'after' becomes 'cli' (I can't explain this - if you can you should believe this answer much more).
'kay' becomes 'k'.
'leaves' suggests deleting specific letters.
'prison' becomes 'nick' (slang term for prison).
'nick' with 'k' taken away is 'nic'.
'cli'+'nic'='CLINIC'

Can you help me to learn more?

(Other definitions for clinic that I've seen before include "Place for specialised treatment, from doctor or politician" , "Medical resource" , "Doctor's session" , "Outpatient session" , "Health centre" .)

I've seen this clue in The Sun.
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